# Vectors - Chapter No 3

Right Answers have been shown below in red color.

1. We say that the displacement of a particle is a vector quantity. Our best justification for this

assertion is:

A) displacement can be specified by a magnitude and a directionB) operating with displacements according to the rules for manipulating vectors leads to results in agreement with experimentsC) a displacement is obviously not a scalarD) displacement can be specified by three numbersE) displacement is associated with motion

2. The vectors a, b, and c are related by c = b − a. Which diagram below illustrates this

relationship?

D is the Right Answer

3. A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude

of the resultant is:

A) zeroB) 1C) 3D) 5E) 7

4. A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:

A) zeroB) 3C) 12D) 47E) 50

5. A vector S of magnitude 6 and another vector have a sum of magnitude 12. The vector T:

A) must have a magnitude of at least 6 but no more than 18B) may have a magnitude of 20C) cannot have a magnitude greater than 12D) must be perpendicular to SE) must be perpendicular to the vector sum

6. The vector −A is:

A) greater than A in magnitudeB) less than A in magnitudeC) in the same direction as AD) in the direction opposite to AE) perpendicular to A

7. The vector V_{3} in the diagram is equal to:

A) V_{1}− V_{2}B) V_{1}+ V_{2}C) V_{2}− V_{1}D) V_{1}cos θE) V_{1}/(cos θ)

8. If |A + B |^{2} = A^{2} + B^{2}, then:

A) A and B must be parallel and in the same directionB) A and B must be parallel and in opposite directionsC) either A or B must be zeroD) the angle between A and B must be 60◦E) none of the above is true

9. If |A + B | = A + B and neither A nor B vanish, then:

A) A and B are parallel and in the same directionB) A and B are parallel and in opposite directionsC) the angle between A and B is 45◦D) the angle between A and B is 60◦E) A is perpendicular to B

10. If |A − B | = A + B and neither A nor B vanish, then:

A) A and B are parallel and in the same directionB) A and B are parallel and in opposite directionsC) the angle between A and B is 45◦D) the angle between A and B is 60◦E) A is perpendicular to B

11. Four vectors (A, B, C, D) all have the same magnitude. The angle θ between adjacent vectors

is 45◦ as shown. The correct vector equation is:

A) A − B − C + D = 0B) B + D − √2C = 0C) A + B = B + DD) A + B + C + D = 0E) (A + C )/√2 = −B

12. Vectors A and B lie in the xy plane. We can deduce that A = B if:

A) A^{2}x + A^{2}y = B^{2}x + B^{2}yB) Ax + Ay = Bx + ByC) Ax = Bx and Ay = ByD) Ay/Ax = By/BxE) Ax = Ay and Bx = By

13. A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and the negative y axis and makes an angle of 30◦ with the x axis. Its y component is:

A) 6/√3B) −6√3C) 6D) −6E) 12

14. If the x component of a vector An, in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is:

A) √3B) 1/2C) √3/2D) 3/2E) 3

15. If A = (6 m)i − (8 m)j then 4A has magnitude:

A) 10 mB) 20 mC) 30 mD) 40 mE) 50 m

16. A vector has a component of 10 m in the +x direction, a component of 10 m in the +y direction, and a component of 5 m in the +z direction. The magnitude of this vector is:

A) zeroB) 15 mC) 20 mD) 25 mE) 225 m

17. Let V = (2.00 m)i + (6.00 m)j − (3.00 m) k. The magnitude of V is:

A) 5.00 mB) 5.57 mC) 7.00 mD) 7.42 mE) 8.54 m

18. A vector in the xy plane has a magnitude of 25 m and an x component of 12 m. The angle it makes with the positive x axis is:

A) 26◦B) 29◦C) 61◦D) 64◦E) 241◦

19. The angle between A = (25 m)i + (45 m)j and the positive x axis is:

A) 29◦B) 61◦C) 151◦D) 209◦E) 241◦

20. The angle between A = (−25 m)i + (45 m)j and the positive x axis is:

A) 29◦B) 61◦C) 119◦D) 151◦E) 209◦